Wigner function and the successive measurement of position and momentum

TYPETheor./Math. Physics Seminar
Speaker:Professor Pier Mello
Affiliation:UNAM, Mexico
Location:Lewiner Seminar Room (412)
Abstract:Wigner function is a “quasi-distribution” that provides a representation of the state of a quantum mechanical system in the phase space of position
and momentum.
We find a relation between Wigner function and appropriate measurements involving the system position and momentum which generalize the
von Neumann model of measurement.
For this purpose, we introduce two probes coupled successively in time to projectors associated with the system position and momentum. We show
that one can relate Wigner function to Kirkwood joint quasi-distribution of position and momentum, the latter, in turn, being a particular case of
successive measurements.
We first consider the case of a quantum mechanical system described in a continuous Hilbert space, and then turn to the case of a discrete, finitedimensional
Hilbert space.